In recent years, the next-generation spintronics is attracting much attention in which electron spin, which is a small magnet in a magnetic material, is controlled by an electric field instead of a magnetic field; and an example of the next-generation spintronics is a ferromagnetic thin film transistor in which a magnetic material is used for an active layer so that magnetism of the active layer is controlled by a gate voltage. In this arrangement, because most of magnetic materials have a carrier density (about 1022 cm3) of electrons (or holes) as high as metal, if a dielectric material used in semiconductor electronics is used for a gate insulating film, a carrier density cannot be modulated sufficiently. To address this issue, there is proposed an electric-double-layer gated transistor in which an ionic liquid is used to modulate the carrier density in a ferromagnetic material (for example, see Non-Patent Documents 1 and 2).